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So there's a fairly well characterized difference between relative risk and absolute risk for conventional cohort studies, and for many questions, the absolute risk is arguably more appropriate.

Is there an analogous way to measure absolute difference for accelerated failure time models? I suspect there isn't, because these models assume proportional survival times, so the relative measure will be constant, but the absolute measure will vary over time, but I wanted to make sure before I abandoned this line of reasoning.

Would it be possible to do it at a fixed point in time, say the median - and do you think this would be of any value?

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  • $\begingroup$ Just to clarify my understanding: absolute risk of disease is a risk of experiencing an event over a specified interval conditional upon not dieing from other causes (ranges from 0 to 1), whereas the relative risk is a comparison of risks under two different settings (ranges from 0 to $\infty$). Further, the criticism of relative risk is a tendency to exaggerate the deleterious effects of exposures for extremely rare diseases, e.g. a 100-fold risk ratio for a less than 1/1,000,000 incidence is practically negligible. Is this correct? $\endgroup$ – AdamO Jan 3 '18 at 19:03
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As you said the PH assumption prevents evaluating an absolute measure of difference in survival.
If you are interested a method to evaluate adjusted differences in survival percentiles, such as the median, has been recently developed and proposed. I'm reporting below a couple of references. Do not hesitate to contact me if you need further information.

Bottai M, Zhang J. Laplace regression with censored data. Biom J. Aug 2010;52(4):487-503.

Orsini N, Wolk A, Bottai M. Evaluating percentiles of survival. Epidemiology. Sep 2012;23(5):770-771.

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Risk ratios and risk differences are two different measures of association for time-to-event outcomes as observed in cohort studies. Risk ratios are the most commonly presented type of outcome because they are easily estimated from Poisson, logistic, or Cox proportional hazards models. Risk differences, or the difference in absolute risk, while less common, boasts several advantages over the risk ratio in terms of interpretability. For instance, if a 50 year old non-smoking woman's 10 year CVD death risk is 1 (10 events per 1,000 person years) whereas a counterfactually matched 50 year old smoking woman has a 10 year CVD death risk of 2% (20 events per 1,000 person years) the risk difference is 1% but the risk ratio or relative risk is 2 or 100%; people often conflate percentages in this case as a fraction of events to person years $\times 100$ (absolute risk difference) or as a proportional difference (RR1/RR2: unitless).

Absolute risk can definitely be measured even in the presence of censoring. With no censoring or competing risks, logistic regression using the identity link is an additive risk model; the coefficients measure absolute risk difference on the natural scale. Similarly, poisson GLMs with the identity link for the counts using the offset of person-years exposure lead to similar estimates of rate differences on the natural scale. For survival models with censoring, parametric models lead to predictions of risk which can be combined to predict risk differences. For instance, with exponential survival models, the log-rate leads to predicted survival curves at several survival times and the model has efficient CIs. Fully stratified Kaplan Meier curves also provide estimates of risk differences but the calculation of the CIs remains an area of research.

Lastly, survival curves and by extension risk differences can be obtained from Cox models using the smoothed estimates of the baseline hazard function with either the Breslow step estimator or the Schoenfeld residuals.

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